Next up for Azarenka will be top seed Kvitova, who was beaten in a thrilling Australian Open final by Naomi Osaka on Saturday.
"I expect a tough match as she (Kvitova) is currently in top form. For me every match is very important regardless of my opponent's name. I just want to play and to progress," Azarenka said.
The 29-year-old has tumbled down the rankings since the birth of her son Leo and an ensuing custody battle, and is currently the world number 51.
"It's just the beginning of the season and every single match is hard for me," Azarenka added.
Elsewhere, fifth seed Julia Goerges reached round two by beating Greek Maria Sakkari 6-2, 7-5 despite appearing to suffer an ankle injury in the opening set.
The German will next face two-time Grand Slam finalist Vera Zvonareva.